I think there's a nice in-between where the problems are both generally useful and also actually do test some concept relatively directly. Kind of like what Fi

I think there's a nice in-between where the problems are both generally useful and also actually do test some concept relatively directly. Kind of like what FizzBuzz can be like for testing for basic pseudocode programming. Where someone who isn't really thinking about the problem will mess up and go for what seems like the obvious solution on the surface, but someone who understands how to code will eventually realize that the obvious "clever" seeming solution is a trap and they have to do it the plain way. I've found those kinds of problems to be the most fun to deal with. A math specific example I vaguely recall from middle school involved calculating the number of handshakes that would happen in total if everyone in the class shook everyone else's hand once. The path to the solution isn't explicit in the question, and for someone who doesn't already know of combinations/permutations, it takes a bit of abstract logic to construct the necessary expression. Yet it doesn't require particularly advanced math to figure out and tests the student's understanding of how to translate real problems into math. Problems where the word problem is just a literal transcription of an equation are not that useful or fun, but also, I think that it takes getting to a fairly high level of education before the math gets advanced enough to more frequently cover meaningful word problem solving (probabilities and statistics, linear algebra, or differential equations), yet the tools for interpreting such problems need to be taught earlier.